...little purple seed-like things falling around the purple flower and the cemetery? If so what are they?

Flower petals.

...had the silver mirror event and the person got a twin? I have.

Yes, that's one of the outcomes.

...tried getting their children to pick a certain pebble and everytime it either disappears or the child drops it?

Happens sometimes.

...had a new collectible not show on the collectible screen after the child pick it up and brought it to the research hut?

If they brought it into the hut right as it was at the end of its timeline (about to disappear) this can happen. Get them faster and you won't have this problem.

Tess